I have the following discrepancy that satisfies this type of inequality. I want to know if this can be related to some kind of weak convexity. If so, what is the name of this property? Additionally, are there any optimization algorithms based on this property? Any references would be greatly appreciated.
$$ D\left( \theta \mathbf{u} + (1 - \theta) \mathbf{u}', \; \theta \mathbf{v} + (1 - \theta) \mathbf{v}' \right) \leq \alpha \left[ \theta D(\mathbf{u}, \mathbf{v}) + (1 - \theta) D(\mathbf{u}', \mathbf{v}') \right], \quad \text{for}\, \alpha>1. $$
